The study of palaeo‐glacial landforms and sediments can give insights into the nature and dynamics of ice sheets. This is particularly the case with regards to the subglacial record, which is challenging to observe in contemporary glaciated settings and hence remains only partially understood. The subglacial hydrological system is an essential component of ice dynamics, where increased water pressure enhances ice motion and sediment deformation, thus reducing ice‐bed contact. Tunnel valleys are large, sinuous, steep‐sided incisions that, together with smaller scale meltwater channels, indicate subglacial meltwater discharge beneath large ice sheets. Through the use of high‐resolution marine geophysical data, a system of buried and exposed tunnel valleys, possible subglacial or proglacial meltwater channels and palaeo‐fluvial valleys have been identified across the shelf of the Celtic Sea between Ireland and Britain. The presence of steep‐sided and overdeepened tunnel valleys is indicative of a large channelized meltwater drainage system beneath the former Irish Sea Ice Stream, the most extensive ice stream to drain the last British–Irish Ice Sheet. After the rapid ice expansion across the Celtic Sea shelf around 28–26 ka, the tunnel valleys were carved into both bedrock and glacigenic sediments and are associated with rapid ice stream retreat northwards into the Irish Sea Basin between 25.6 and 24.3 ka. The presence of a major subglacial meltwater system on the relatively shallow shelf suggests that significant erosive meltwater discharge occurred during the last deglaciation and highlights the important contribution of meltwater to the retreat of the British–Irish Ice Sheet on the continental shelf.